simple closed curve

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1: 1.6 Vectors and Vector-Valued Functions

… ►The geometrical image $C$ of a path $𝐜$ is called a simple closed curve if $𝐜$ is one-to-one, with the exception $𝐜(a)=𝐜(b)$. … … ►and $S$ be the closed and bounded point set in the $(x,y)$ plane having a simple closed curve $C$ as boundary. …

2: 1.9 Calculus of a Complex Variable

… ►A simple closed contour is a simple contour, except that $z(a)=z(b)$. … ►Any simple closed contour $C$ divides $ℂ$ into two open domains that have $C$ as common boundary. … ►If $f(z)$ is continuous within and on a simple closed contour $C$ and analytic within $C$, then … ►If $f(z)$ is continuous within and on a simple closed contour $C$ and analytic within $C$, and if $z_0$ is a point within $C$, then …

3: 10.21 Zeros

… ►Each curve that represents an infinite string of nonreal zeros should be located on the opposite side of its straight line asymptote. … ►In Figures 10.21.1, 10.21.3, and 10.21.5 the two continuous curves that join the points $\pm 1$ are the boundaries of $𝐊$, that is, the eye-shaped domain depicted in Figure 10.20.3. These curves therefore intersect the imaginary axis at the points $z=\pm \mathrm{i}c$, where $c=0.66274\mathrm{\dots }$. … ►In Figures 10.21.2, 10.21.4, and 10.21.6 the continuous curve that joins the points $\pm 1$ is the lower boundary of $𝐊$. … ►are simple and the asymptotic expansion of the $m$th positive zero as $m\to \mathrm{\infty }$ is given by …

4: 18.39 Applications in the Physical Sciences

… ►where the orthogonality measure is now $dr$, $r\in [0,\mathrm{\infty }).$ … ►Orthogonality, with measure $dr$ for $r\in [0,\mathrm{\infty })$, for fixed $l$ … ►normalized with measure $r^{2}dr$, $r\in [0,\mathrm{\infty })$. … ►Here tridiagonal representations of simple Schrödinger operators play a similar role. … ►which maps $ϵ\in [0,\mathrm{\infty })$ onto $x\in [-1,1]$. …